Hanging a brick free over an edge by stacking them National Geographics TV has a series called "None of the above". In one episode the presenter shows that by stacking 4 bricks (here shown as 'xxxxxxxx') you can have one of the bricks completely hang free of the edge:
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It barely hangs free, but it does work if you are careful. I have found a more efficient way also using only 4 bricks:
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This will let the brick be much further out. This gets me to think: Is there an even more efficient method - either using fewer bricks or a different way of stacking to shift the brick even further out? How do I compute the optimal shift lengths of each brick?
Edit:
After a few more experimentations it seems the optimal is symmetrical:
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The lower brick will be at 50% over the edge. The two middle bricks will be pulled as far out as they can before they drop. So the hard part seems to be computing how far it can be pulled out. Experimentally it is around 1/3.
 A: I will help you solve a general stability problem for an overhanging sandwiched block.

Say blocks all have length $\ell$ and weight $W$ at their center. The overhanging block, touches the block below it at a distance $a$ from the edge, and a force $F$ is applied from the blocks above, and a reaction $R$ acts from below.
The minimum required force $F$ above to keep the block stable is $$F\gt W \left( \frac{\ell}{2 a} - 1\right)$$
So for example if you place four blocks above, with $F=2 W$ since it is sharing 50% of their load, then the minimum overlap distanc is $a>\frac{\ell}{6}$. Please try it and see if this works. I have ignored friction which adds to the stability so the above is conservative.
A: It looks like this exact question popped out recently in almost all webpages I use to visit. 
I encountered this problem in this video where they provide a friendly approach to the problem and several solutions. 
In this and this articles, some constructions are provided and conclude that the symmetrical structure (which requires $n$ bricks resulting in an overhang $\sim \ln(n)$) is not the optimal structure. They prooved also that the optimal structure will overhang $\sim n^{\frac{1}{3}}$, and they give an explicit example called parabolic stack:

